A social network emerges by drawing lines to represent connections within the household (a) and from the household members to their direct contacts (b). Connecting those individuals to their own circle of contacts (c) and those to the next generation of contacts (d) enlarges the network. Long-distance connections show contacts who also know each other. Yet no one in this network has more than 15 direct contacts, meaning none is a highly connected "hub" of society. One insight from this work is that so many alternative paths can connect any pair of people, isolating only hub individuals would do little to restrict the spread of infectious disease through this population.
The shape of this small network expands with each generation of contacts. A disease moving through such a population therefore infects rising numbers of people in each generation of transmission.
a people in a population, could somehow be identified and treated or removed from the network, the reasoning goes, then an epidemic could be halted without having to isolate or treat everyone in the population. But our analyses of the social networks used by EpiSims suggest that society is not so easily disabled as physical infrastructure.
The network of physical locations in our virtual Portland, defined by people traveling between them, does indeed exhibit the typical scale-free structure, with certain locations acting as important hubs. As a result, these locations, such as schools and shopping malls, would be good spots for disease surveillance or for placing sensors to detect the presence of biological agents.
The urban social networks in the city also have human hubs with higher than average contacts, many because they work in the physical hub locations, such as teachers or sales clerks. Yet we have also found an unexpectedly high number of "short paths" in the social networks that do not go through hubs, so a policy of targeting only hub individuals would probably do little to slow the spread of a disease through the city.
In fact, another unexpected property we have found in realistic social networks is that everyone but the most devoted recluse is effectively a small hub. That is to say, when we look at the contacts of any small group, such as four students, we find that they are always connected by one hop to a much larger group. Depicting this social network structure results in what is known as an expander graph [see box on opposite page], which has a cone shape that widens with each hop. Its most important implication for epidemiology is that diseases can disseminate exponentially fast because the number of people exposed in each new generation of transmission is always larger than the number in the current generation.
Theoretically, this should mean that whatever health officials do to intervene in a disease outbreak, speed will be one of the most important factors determining their success. Simulating disease outbreaks with EpiSims allows us to see whether that theory holds true.
Smallpox Attack after we began developing EpiSims in 2000, smallpox was among the first diseases we chose to model because government officials charged with bioterror-ism planning and response were faced with several questions and sometimes conflicting recommendations. In the event that smallpox was released into a U.S. population, would mass vaccination be necessary to prevent an epidemic? Or would targeting only exposed individuals and their contacts for vaccination be enough? How effective is mass quarantine? How feasible are any of these op tions with the existing numbers of health workers, police and other responders?
To answer such questions, we constructed a model of smallpox that we could release into our synthetic population. Smallpox transmission was particularly difficult to model because the virus has not infected humans since its eradication in the 1970s. Most experts agree, though, that the virus normally requires significant physical contact with an infectious person or contaminated object. The disease has an average incubation period of approximately 10 days before flulike symptoms begin appearing, followed by skin rash. Victims are contagious once symptoms have appeared and possibly for a short time before they develop fever. Untreated, some 30 percent of those infected would die, but the rest would recover and be immune to reinfection.
Vaccination before exposure or within four days of infection can stop small pox from developing. We assumed in all our simulations that health workers and people charged with tracking down the contacts of infected people had already been vaccinated and thus were immune. Unlike many epidemiological models, our realistic simulation also ensures that the chronology of contacts will be considered. If Ann contracted the disease, she could not infect her co-worker Bob a week earlier. Or, if Ann does infect Bob after she herself becomes infected and if Bob in turn infects his family member Cathy, the infection cannot pass from Ann to Cathy in less than twice the min-
imum incubation period between disease exposure and becoming contagious.
With our disease model established and everyone in our synthetic population assigned an immune status, we simulated the release of smallpox in several hub locations around the city, including a university campus. Initially, 1,200 people were unwittingly infected, and within hours they had moved throughout the city, going about their normal activities.
We then simulated several types of official responses, including mass vaccination of the city's population or contact tracing of exposed individuals and their contacts who could then be targeted for vaccination and quarantine. Finally, we simulated no response at all for the purpose of comparison.
In each of these circumstances, we also simulated delays of four, seven and 10 days in implementing the response after the first victims became known. In
CHRIS L. BARRETT, STEPHEN G. EUBANK and JAMES P. SMITH worked for five years together at Los Alamos National Laboratory (LANL) to develop the EpiSims simulation. Barrett, who oversaw a predecessor project, TRANSIMS, is a bioinformatics specialist who now directs the Simulation Science Laboratory at the Virginia Bioinformatics Institute (VBI) in Blacksburg. Eubank, a physicist, is deputy director of the VBI simulation lab and was EpiSims team leader at Los Alamos. Smith, also a physicist, continues to work with simulations related to TRANSIMS as the project office leader for Discrete Simulation Science in the LANL Computer and Computational Sciences Division.
Our analyses suggest that society is not so easily disabled as infrastructure.
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